00:01
Hi, in this problem it is given that f is equal to 2y i plus 2 z j plus 9 x z k.
00:14
Now let us consider that integral i is equal to double integral del w f .d.
00:25
So we have to evaluate this integral for each.
00:30
So now we can write double integral del w f dot d s equal to triple integral divergence f dv.
00:45
So for this f we have divergence of f equal to 9x.
00:53
Now in the first part a we are given that z lies between xxxx plus y square to 1.
01:06
Therefore, we can write integral i equal to double integral x square plus y square less than equal to 1 and the integral x square plus y square to 1, 9x, d z, dy, d x, d x.
01:28
Now integrating with respect to z, we obtain the value of i equal to double integral x square plus y square less than equal to 1 that is this is our region and 9x into 1 minus x square plus y square into divide d x now using the polar coordinates x equal to r cos theta and y equal to r sine theta we can write i equal to integral 0 2 pi integral 0 to 1 9 r cos theta into 1 minus r square dr, d theta.
02:07
And further integrating this, we obtain the value of double integral del w.
02:13
F dot, ds equal to 0.
02:17
Now, in the next part b, we are given that z lies between x square plus y square to 1 and x is greater than equal to 0.
02:31
Now, following the same procedure as we have done in part a, we obtain the integral i equal to integral 0 to 1 integral minus pi by 2 to pi by 2...